Time series analysis and signal estimation/prediction has been used in a variety of applications, including surveillance and data analysis. In time series analysis, one of the most challenging problems is to predict the signals generated by nonlinear dynamic systems since analytical models/functions for such signals may not exist, which means one cannot describe their functions with existing well-known functions. Most existing techniques use neural networks and fuzzy inference systems to approximate their functions in order to predict these kinds of signals.
Existing techniques for such systems include the Adaptive-Network-Based Fuzzy Inference System (ANFIS) and the Dynamic Evolving Neural-Fuzzy Inference System (DENFIS). ANFIS was described by Jyh-Shing Roger Jang in a publication entitled, “ANFIS: Adaptive-Network-Based Fuzzy Inference System,” as published in IEEE Transactions on Systems, Man, and Cybernetics, vol. 23, no. 3, pp. 665-685, 1993. Alternatively, DENFIS was described by Nikola K. Kasabov and Qun Song in a publication entitled, “DENFIS: Dynamic Evolving Neural-Fuzzy Inference System and Its Application for Time-Series Prediction,” as published in IEEE Transactions on Fuzzy Systems, vol. 10, no. 2, pp. 144-154, 2002.
The existing techniques are generally very complicated and are not flexible to the changes of prediction horizon of the signals. In both the ANFIS and DENFIS systems, the mapping networks are trained for a specific prediction step. Thus, in order to make a prediction for different prediction steps, their networks have to be retrained, making the systems ineffective for multi-step predictions. Additionally, the systems are unable to efficiently predict signals whose analytic functions may not exist, such as chaotic signals.
Thus, a continuing need exists for a system to predict signals (time series), including signals generated by linear/nonlinear dynamic systems and signals corrupted by random noises. A need also exists for a system that can make multi-step predictions without retraining its nonlinear mapping function.